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We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the…
The probabilistic method is a technique for proving combinatorial existence results by means of showing that a randomly chosen object has the desired properties with positive probability. A particularly powerful probabilistic tool is the…
We consider the problem of protecting and manipulating elections by recounting and changing ballots, respectively. Our setting involves a plurality-based election held across multiple districts, and the problem formulations are based on the…
We study strategic candidate nomination by parties in elections decided by Plurality voting. Each party selects a nominee before the election, and the winner is chosen from the nominated candidates based on the voters' preferences. We…
A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial…
Participatory budgeting (PB) has been widely adopted and has attracted significant research efforts; however, there is a lack of mechanisms for PB which elicit project interactions, such as substitution and complementarity, from voters.…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
This paper formalizes the lattice structure of the ballot voters cast in a ranked-choice election and the preferences that this structure induces. These preferences are shown to be counter to previous assumptions about the preferences of…
In this paper, I introduce a novel stability axiom for stochastic voting rules, called self-equivalence, by which a society considering whether to replace its voting rule using itself will choose not to do so. I then show that under the…
The classical Hilbert specialization property is a field-theoretic tool ensuring that polynomial irreducibility over a field is preserved under specialization of some of the variables. We develop an integral counterpart by introducing the…
An important -- but very demanding -- property in collective decision-making is strategyproofness, which requires that voters cannot benefit from submitting insincere preferences. Gibbard (1977) has shown that only rather unattractive rules…
In the first part of the paper boundary-value problems are considered under weak assumptions on the smoothness of the domains. We assume nothing about smoothness of the boundary $\partial D$ of a bounded domain $D$ when the homogeneous…
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
This paper develops a method to use singles' data in a non-parametric revealed preference setting of collective household choice. We use it to test the controversial assumption of preference stability between singles and couples, without…
We investigate the allocation of children to childcare facilities and propose solutions to overcome limitations in the current allocation mechanism. We introduce a natural preference domain and a priority structure that address these…
We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…
Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such…